Profile Monitoring of Probability Density Functions via Simplicial Functional PCA With Application to Image Data

<p>The advance of sensor and information technologies is leading to data-rich industrial environments, where large amounts of data are potentially available. This study focuses on industrial applications where image data are used more and more for quality inspection and statistical process monitoring. In many cases of interest, acquired images consist of several and similar features that are randomly distributed within a given region. Examples are pores in parts obtained via casting or additive manufacturing, voids in metal foams and light-weight components, grains in metallographic analysis, etc. The proposed approach summarizes the random occurrences of the observed features via their (empirical) probability density functions (PDFs). In particular, a novel approach for PDF monitoring is proposed. It is based on simplicial functional principal component analysis (SFPCA), which is performed within the space of density functions, that is, the Bayes space <i>B</i>². A simulation study shows the enhanced monitoring performances provided by SFPCA-based profile monitoring against other competitors proposed in the literature. Finally, a real case study dealing with the quality control of foamed material production is discussed, to highlight a practical use of the proposed methodology. Supplementary materials for the article are available online.</p

Weighted Functional Data Analysis for the Calibration of a Ground Motion Model in Italy

Motivated by the crucial implications of Ground Motion Models in terms of seismic hazard analysis and civil protection planning, this work extends a scalar Ground Motion Model for Italy to the framework of Functional Data Analysis. The inherent characteristic of seismic data to be incomplete over the observation domain of oscillation periods entails embedding the analysis in the context of partially observed functional data and performing data reconstruction. This work proposes a novel methodology that accounts for the fact that parts of the curves are directly observed and other parts are reconstructed, thus characterized by greater uncertainty. The method defines observation-specific functional weights, which enter the estimation process to reduce the impact that the less reliable portions of the curves have on the final estimates. The classical methods of smoothing and concurrent functional regression are extended to include weights. The advantages of the proposed methodology are assessed on synthetic data. Eventually, the weighted functional analysis performed on seismological data is shown to provide a natural smoothing and stabilization of the spectral estimates of the Ground Motion Model considered.</p